Question

The ratio of the value of g in SI units to CGS units is.
A. ${10^2}$:1
B. 10:1
C. $10^{-1}$:1
D. $10^{-2}$:1

Answer 1

Hint: g is the symbol of acceleration due to gravity. The value of g varies if the gravitational force of the body is changed. SI unit of measurement is the international standard of the measurement. This unit system is accepted world-wide. The CGS system of the measurement is known as the centimeter gram and second system. In this system, the unit of length is meter, unit of mass is gram and unit of time is second.

Complete step by step answer:
The acceleration due to gravity is represented by g. The unit of g in International standard is meter per square second. It is symbolically given as, $\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$ .
The value of g is $9.8\ \dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$.
The CGS unit for length is centimeter. The CGS unit for time is second.
Converting SI unit into CGS unit we get,
$\Rightarrow 9.8\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}=9.8\times \dfrac{\text{100cm}}{{{\text{s}}^{\text{2}}}}$
So, in SI unit acceleration due to gravity is $9.8\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$.
In CGS unit acceleration due to gravity is $980\dfrac{\text{cm}}{{{\text{s}}^{\text{2}}}}$.
Taking ratio of SI and CGS unit of acceleration due to gravity we get,
\[\begin{align}
  & \Rightarrow 9.8\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}:980\dfrac{\text{cm}}{{{\text{s}}^{\text{2}}}}=1:100 \\
 & \Rightarrow 9.8\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}:980\dfrac{\text{cm}}{{{\text{s}}^{\text{2}}}}=1:{{10}^{2}} \\
\end{align}\]
Correct option is D.

Note:
The acceleration due to gravity of Earth can be calculated using the given formula.
$\Rightarrow g=\dfrac{GM}{{{\left( R+h \right)}^{2}}}$
Where,
G is the gravitational constant
M is the mass of the Earth.
R is the radius of the Earth.
h is the height from the surface of Earth.